PV Function

Changes and Enhancements

PV Function

calculates the present value of a vector of cash flows and returns a scalar

PV( times,flows,freq,rates)

The PV function returns a scalar containing the present value of the cash flows based on the specified frequency and rates.

times: is an n ×1 column vector of times. Elements should be non-negative.
flows: is an n ×1 column vector of cash flows.
freq: is a scalar that represents the base of the rates to be used for discounting the cash flows. If positive, it represents discrete compounding as the reciprocal of the number of compoundings. If zero, it represents continuous compounding. If -1, it represents per-period discount factors. No other negative values are allowed.
rates: is an n ×1 column vector of rates to be used for discounting the cash flows. Elements should be positive.

A general present value relationship can be written as

$P=\sum_{k=1}^K c(k) D(t_k)$

where P is the present value of the asset, {c(k)}k = 1, ... ,K is the sequence of cash flows from the asset, t_k is the time to the k-th cash flow in periods from the present, and D(t) is the discount function for time t.

With per-unit-time-period discount factors d_t:

D(t) = d_t^t

With continuous compounding:

$D(t)=e^{-r_t t}$

With discrete compounding:

D(t) = (1+fr)^-t/f

where f > 0 is the frequency, the reciprocal of the number of compoundings per unit time period.

The following code presents an example of the PV function:

   timesn=T(do(1,100,1)); 
   flows=repeat(10,100); 
   freq=50;
   rate=repeat(0.10,100); 
   pv=pv(timesn,flows,freq,rate);  
   print pv;

The result is

   PV
   266.4717

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